It does sound like Travis to me. IIRC , juror 13 has some of TA's journal entries on her site you might want to read if you haven't already.
TA was a huge fan of personal development books, ideas, truisms. The note reads that way to me. The other context is that she demanded he send her one, and that demand came along with "asking" him to do other favors for her around the same time, which was very shortly after she was forced into exile.
Travis was not liking that



very much, was increasingly expressing anger and impatience with her non-stop crap which he'd had some silly notion would CEASE after he'd finally gotten rid of her.
The note says to me he was giving her the best he could offer to her demand for "sweet." That she MOVE ON. That she leave behind the need she felt to be so nasty and ugly and psycho and fake suicidal and stalky....all of it, and let her "better self" emerge.
IMO the note couldn't be any more Travis and less her.
PS. The note is signed- "Sincerely yours, Travis"